Can a mono molecular blade or point puncture advanced carbon armour?

Question

In the previous post, I asked what would happen if armour outpaced modern firearms. The answers I received are all very interesting. There is one point that comes up however that I never considered. And that was that there would the distinct possibility that melee would return in the form of maxes and war hammers. But knights also used rondel daggers to go through weak points like joints and half sword technique to allow the point to go through the visor.

So what I’m saying asking is; Can a Mono molecular point go through the weak points of advanced carbon armour like the joints? And considering that this mono molecular technology, can it cut as well?

EDIT: the blade itself is a steel blade that has advanced carbon materials in the crystalline matrix in order for it to hold a mono-edge

Answer 1

So, one effect which is easily neglected when arguing a direct comparison in the strengths of the two materials is that thickness does matter. Whilst it is true that Newton's 3rd law must hold, and that the force applied by the dagger must also be applied onto the dagger by the armour is true. It is a false conclusion, however, that the strongest material wins. Without knowing the details of your armour and knife, it's hard for me to give exact numbers and information on this, but I'll see what I can do.

Firstly, however, I'll defend my point about the fact that the sharpness matters. Let's imagine this on a molecular level. No structure is ever a perfectly homogenous material, and so for every stab-attempt you make, you'll likely encounter different molecular spacings and bond strengths, so, for simplicity, I'm going to assume that your blade is straight, and has a large length compared to the inter-atomic spacings, in both it's height and length, if not thickness. In this simplified scenario, we could consider it acting to push two rows of molecules apart. However, because, for the sake of the model, these two rows are many orders of magnitude longer than the area of blade connecting with armour, we can assume, for the sake of an easy life, that the blade is cutting an infinitely long line. At this point, it doesn't matter which point along the blade you begin to cut, effects from all points in the line cancel, and we are left being able to consider only 3 atoms. One, the atom in the blade, and the other two being the atoms either side of that point of the blade.

At a particular average bond length, there will be a related force holding the atoms of the armour together. However, we're imagining that our blade is cutting between atoms, which means that the armour is not simply pushing back, but is also pushing the atom from both sides with equal and opposite forces which completely cancel. This is not to say that material strength doesn't come into play, but, the smaller the blade is, the higher liklihood it has of getting into a weakness without blunting in a head-on collision. So, how much force do we need to apply?

Well, it depends on how the blade tapers. If we could design something thin enough to pass between atoms, that'd be great, and, in fact, such a particle already exists: neutrinos. However, there's a very good reason that they're not used in nano-knives! The very thing that means they can pass through other matter is the fact that they don't interact much with it - but if they don't interact well with other matter, they won't do any damage once they've passed through.

So, we're going to need to make a hole large enough to do some damage, and a knife will help us to do that, by providing 'mechanical advantage'. In other words, by drawing out a force over a longer distance, just like taking a gentle walk to the top of a hill rather than a steep one. A blade reduces the average force required, but we'd still need to apply the same energy to create a hole of equivalent size in the body armour, so a better option would be using a blade to create a hole, which then retracts and pushes something, a poison, a small explosive, an extendable knife, through the hole - one thing creates the breach, the next does the damage. A simpler method, requiring less nanoengineering is to simply, once a hole has been made, to wiggle the knife around. However, assuming that the body armour is relatively thick, this would most likely break the point of your knife, or require a large enough hole that you've had to put in enough energy to not make it worth your while in the first place.

So, some numbers. A single carbon-carbon double bond, such as that found in diamond has a strength of around 400kJ/mol, meaning to break it would require 400000J of energy, for every 6.03*10^23 atoms. That may seem like not a lot, but the density of diamond is about 6g/cm^3, corresponding to 200kJ being required to break a single cubic centimeter of such bonds. And, for a structure like diamond, we probably would need to break that many. Most carbon structures are so strong, not because of their bond strengths, but because there bonds don't deform before breaking like most metals do. So, for some maths.

Assuming you have a blade strong enough to act like a wedge between two atoms, and you get lucky enough to line it up with some atoms, then, assuming it's easy to damage the human body beneath, compared to the body armour, in order to damage a conical section of a sphere in the body, with a half-angle of t, in body armour of thickness l, made primarily out of carbon, you'd need to make a hole of radius (l/2)*tan(t). This would involve breaking a cylinder of bonds, of volume $\pi r^2 l$, which would correspond to an energy of $E = \pi r^2 l \times (200000000 J m^{-3})$. No matter the slope of your blade, you'd still have to put in around this much energy (I'm assuming no deformation occurs, which isn't true, but this gives the picture).

However, nothing here says anything about the radius of the sphere in which a person could be stabbed, and it's that this determines if they've been killed, right? This leads us to our main result from this:

As long as you are able to penetrate the body armour with a long enough point with side-on structural rigidity, you should be able to wiggle it around to do enough damage to the person to kill them.

In practice, however, all of this would be really hard to achieve in a fight, because the odds of a single blade aligning over a long enough area is pretty low, and if it doesn't align well, then it does just come down to a competition between materials.

The largest problem with any of this is the molecular blade itself, however. And, most likely, simply chemical reactions would dull it, with oxygen radicals in the air bonding to the tip of the blade to remove its fine point. It would still be a pretty sharp blade, and would magnify the force in proportion to the pressure exerted, but it wouldn't be able to get between molecules any more, no matter how lucky you got.

I feel like I've just rambled, but hopefully you get something out of this!

Answer 2

If the sword is harder than the armor, yes. A sword is nothing more than a machine at work - it converts the impact from a large area to a small area, thus increases the force. Compare a sword to a hammer. If you swing both with the same force, all that's really happening is the force of the sword is affecting a much small area. And since the force is so strong, the sword obliterates the connections in that area, and cuts through it.

However, this is where Newton's Third Law takes effect - every action has an equal and opposite reaction. Any force the sword exerts is, in turn, exerted back upon the sword through the object it makes contact with. This isn't a problem, because the sword is the stronger of the two objects, usually. A knife through butter, for instance, or a butcher's knife through flesh will both cut through the material.

So let's zoom in on your mono-molecular weapon. When the line of molecules hit the armor, the force of your entire swing with be condensed into that line of molecules, creating an incredibly powerful force multiplier. When the molecules hit, Newton's Law provides the reaction, and now on that single line of molecules, your sword vs the armor, both are pressing against each other equally (from a physics perspective). So whichever is the stronger one wins.

Rondel daggers weren't use to punch through armor though - like I explained in this answer, punching through metal wasn't easy, you needed a thoroughly superior metal and a lot of force. They were use to burst links in chain mail, or otherwise stab at exposed spots. A good tactic against armor wearers, but you don't need a mono-molecular blade to do that. Also, your blade will cut exceptionally, though be careful. The sword's own weight will let it cut through anything the edge is leaned against.